Higher November 2021 Paper 1 Q5
5 Yasmin has some identical rectangular tiles.
Each tile is \(L\) cm by \(W\) cm.
Diagram NOT accurately drawn
Using 9 of her tiles, Yasmin makes rectangle \(ABCD\), shown in the diagram below.
Diagram NOT accurately drawn
The area of \(ABCD\) is 1620 cm2
Work out the value of \(L\) and the value of \(W\).
(5)
| Scheme | Marks |
|---|---|
\(LW = 180\) oe \((9LW = 1620)\) or \(4L \times (L + W) = 1620\) oe or \(5W \times (L + W) = 1620\) oe or \(4L = 5W\) oe \(\left(L = \dfrac{5}{4}W\right.\) oe or \(\left.W = \dfrac{4}{5}L \text{ oe}\right)\) | M2 |
\(L \times \text{``}\dfrac{4}{5}L\text{''} = \text{``}{180}\text{''}\) oe or \(W \times \text{``}\dfrac{5}{4}W\text{''} = \text{``}{180}\text{''}\) oe or \(4L \times \left(L + \dfrac{4}{5}L\right) = 1620\) oe or \(5W \times \left(\dfrac{5}{4}W + W\right) = 1620\) oe or \(9L\left(\text{``}\dfrac{4}{5}L\text{''}\right) = 1620\) oe or \(9\left(\text{``}\dfrac{5}{4}W\text{''}\right)W = 1620\) oe or \(4\left(\text{``}\dfrac{180}{W}\text{''}\right)^2 + 4(\text{``}{180}\text{''}) = 1620\) oe or \(5(\text{``}{180}\text{''}) + 5\left(\text{``}\dfrac{180}{L}\text{''}\right)^2 = 1620\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(L = 15\) and \(W = 12\) | A2 |
| (5) | |
| (5 marks) |
Notes
M2: for any two correct equations from
(i) \(LW = 180\) oe \((9LW = 1620)\)
(ii) \(4L \times (L + W) = 1620\) oe
(iii) \(5W \times (L + W) = 1620\) oe
(iv) \(4L = 5W\) oe \(\left(L = \dfrac{5}{4}W\right.\) oe or \(\left.W = \dfrac{4}{5}L \text{ oe}\right)\)
(M1 for one correct equation or 1620 ÷ 9 (= 180))
M1: for a correct equation in terms of one variable only
A2: for both correct
(A1 for one correct)
Award 4 marks for \(L = 12\) and \(W = 15\) dep on M3